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Journal Article

A Shortcut to the Q-Operator

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons2679

Meneghelli,  Carlo
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20717

Staudacher,  Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1005.3261v2.pdf
(Preprint), 503KB

1742-5468_2010_11_P11002.pdf
(Any fulltext), 666KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Bazhanov, V., Lukowski, T., Meneghelli, C., & Staudacher, M. (2010). A Shortcut to the Q-Operator. Journal of Statistical Mechanics, 2010(11): P11002. doi:10.1088/1742-5468/2010/11/P11002.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-69EA-6
Abstract
Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare and differentiate our approach to earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT.